The first stage DIT-FFT of a sequence x(n) is given by:
A. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]
B. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]
C. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]
D. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( {k + N} \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]
Answer: Option C
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
The Fourier transform of a real valued time signal has
A. Odd symmetry
B. Even symmetry
C. Conjugate symmetry
D. No symmetry
A. $$V$$
B. $${{{T_1} - {T_2}} \over T}V$$
C. $${V \over {\sqrt 2 }}$$
D. $${{{T_1}} \over {{T_2}}}V$$
A. $$T = \sqrt 2 {T_s}$$
B. T = 1.2Ts
C. Always
D. Never
A. $${{\alpha - \beta } \over {\alpha + \beta }}$$
B. $${{\alpha \beta } \over {\alpha + \beta }}$$
C. α
D. β
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